With inclusion of straight flush and royal flush, there are $10$ ways of getting a straight in a single suit and each of the $5$ cards that form a straight has $4$ different suits. Hence, there are $10\cdot4^5 = 10,240$ ways to get a straight in a 5-card poker game. There are a total of ${52}\choose{5}$$= 2,598,960$ ways of getting a unique hand therefore the $\Pr(\text{straight}) =\displaystyle \frac{10,240}{2,598,960} \approx 0.39\%.$
This is the probability for a single player. But if there are more than one player, can I assume that the events that the players are getting a straight is mutually independent from each other hence
$$ \Pr(\text{straight}_{player_1}\cup \text{straight}_{player_2}\cup\ldots\cup \text{straight}_{player_n}) = \Pr(\text{straight}_{player_1})+ \Pr(\text{straight}_{player_2}) +\ldots + \Pr(\text{straight}_{player_n})$$
My first intuition is that it is mutually independent for players $\leq4$ since there are four suits that may still give each players a chance of getting a straight. But a part of me thinks that a player getting a straight may affect the other players chance of getting a straight.
What could it be?